По неравенству Коши-Буняковского
![S^2 \leq (3^2+(-1)^2)(sin^2A+cos^2A) = 10 \cdot 1 = 10 \\ |S| \leq \sqrt{10}\\ S \leq \sqrt{10}](https://tex.z-dn.net/?f=S%5E2+%5Cleq+%283%5E2%2B%28-1%29%5E2%29%28sin%5E2A%2Bcos%5E2A%29+%3D+10+%5Ccdot+1+%3D+10+%5C%5C+%7CS%7C+%5Cleq+%5Csqrt%7B10%7D%5C%5C++S+%5Cleq+%5Csqrt%7B10%7D)
Ответ
1 . log0,4(16) - 2log0,4(10) = log0,4(16) - lig0,4(10)² = log0,4{16/100)=
=log0,4(0.4)² = 2·log0,4(0,4)= 2·1= 2
2. = log0,5(125) - log0,5(10³)= log0,5(125/1000)= log0,5( 0,5³)= 3
3. =log6(3²) + log6[(1/4)^(-1)]= log6(9)+log6(4)= log6(6²)= 2
4. =log0,3(3³) - 3log0,3(10) = 3·(log0,3(3) - log0,3(10) =
= 3·log0,3(3/10) = 3·1= 3
2y=3x-5. подставляем во 2 уравнение: 5x+2*(3x-5)=1; 5x+6x-10=1; 5x+6x=1+10; 11x=11; x=11/11=1. 2y=3*1-5, 2y= -2, y=(-2)/2= -1. Ответ: (1: -1).